if you have a 15 ft ladder and angle it 75 degrees how far from the house will the base of the ladder be
To find how far from the house the base of the ladder will be, you can use trigonometry. Let's call the distance from the base of the ladder to the house as 'x'.
We have a right triangle formed by the ladder, the distance from the base to the house (x), and the height of the ladder (15 ft). The angle between the ladder and the ground is 75 degrees.
In a right triangle, the side opposite to an angle is called the opposite side, and the side adjacent to the angle is called the adjacent side.
In this case, the opposite side is the height of the ladder (15 ft), and the adjacent side is the distance from the base to the house (x).
We can use the trigonometric function tangent (tan) to find the relationship between these two sides:
tan(angle) = opposite/adjacent
tan(75 degrees) = 15 ft/x
To solve for x, we rearrange the equation:
x = 15 ft / tan(75 degrees)
Now, let's calculate the value of x using a calculator or a math tool:
x ≈ 3.732 ft
Therefore, the base of the ladder would be approximately 3.732 feet from the house.